Free energy and active inference Karl Friston

1. 3rd IMPRS NeuroCom Summer School, Leipzig, Germany10 - 12 July 2013 Free energy and active inference Karl Friston Abstract How much about our interaction with – and experience of – our world can be deduced from basic principles? This talk reviews recent attempts to understand the self-organised behaviour of embodied agents, like ourselves, as satisfying basic imperatives for sustained exchanges with the environment. In brief, one simple driving force appears to explain many aspects of action and perception. This driving force is the minimisation of surprise or prediction error that – in the context of perception – corresponds to Bayes-optimal predictive coding (that suppresses exteroceptive prediction errors) and – in the context of action – reduces to classical motor reflexes (that suppress proprioceptive prediction errors). We will look at some of the phenomena that emerge from this principle; such as hierarchical message passing in the brain and the perceptual inference that ensues. These perceptual abilities rest upon prior beliefs about the world – but where do these beliefs come from? We will consider recent proposals about the nature of prior beliefs and how they underwrite active sampling of the sensorium. Put simply, to minimise surprising states of the world, it is necessary to sample inputs that minimise uncertainty about the causes of sensory input. When this minimisation is implemented via prior beliefs – about how we sample the world – the resulting behaviour is remarkably reminiscent of visual searches and other forms of active inference. In short, if percepts correspond to hypotheses, then action could be construed as sampling data to test perceptual hypotheses – and accrue evidence for our very existence. I hope to illustrate these points using simulations of action observation and saccadic eye movements.

2. Active inference and predictive coding Active inference and action observation Active inference and saccadic searches

3. “Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism” - von Helmholtz Hermann von Helmholtz Richard Gregory Geoffrey Hinton From the Helmholtz machine to the Bayesian brain and self-organization Thomas Bayes Richard Feynman Ross Ashby

4. How do we minimize prediction errors (free energy)? sensations – predictions Prediction error Change predictions Change sensations Action Perception

5. Action as inference – the “Bayesian thermostat” Posterior distribution Prior distribution Likelihood distribution 20 40 60 80 100 120 temperature Perception Action

6. From models to perception A simple hierarchy Generative model Descending predictions Model inversion (inference) Expectations: Ascending prediction errors Predictions: Prediction errors:

7. David Mumford Predictive coding with reflexes Action oculomotor signals reflex arc proprioceptive input pons Perception retinal input Prediction error (superficial pyramidal cells) frontal eye fields geniculate Top-down or backward predictions Conditional predictions (deep pyramidal cells) Bottom-up or forward prediction error visual cortex

8. Prediction error can be reduced by changing predictions (perception) Prediction error can be reduced by changing sensations (action) Perception entails recurrent message passing in the brain to optimize predictions Action fulfils descending predictions

9. Action as inference – the “Bayesian thermostat” Prior distribution 20 40 60 80 100 120 temperature Perception: Action:

10. Action with point attractors visual input Exteroceptive predictions Descending proprioceptive predictions proprioceptive input

11. Heteroclinic cycle (central pattern generator) Descending proprioceptive predictions action observation 0.4 0.6 0.8 position (y) 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 position (x) position (x)

12. If percepts are hypotheses, where do we look for evidence? Richard Gregory

13. Sampling the world to minimise uncertainty Free energy minimisation minimise uncertainty visual input stimulus salience sampling Perception as hypothesis testing – saccades as experiments

14. Parietal (where) Frontal eye fields Visual cortex Pulvinar salience map Fusiform (what) oculomotor reflex arc Superior colliculus

15. Saccadic eye movements Saccadic fixation and salience maps Hidden (oculomotor) states Visual samples Conditional expectations about hidden (visual) states And corresponding percept

16. Hermann von Helmholtz “Each movement we make by which we alter the appearance of objects should be thought of as an experiment designed to test whether we have understood correctly the invariant relations of the phenomena before us, that is, their existence in definite spatial relations.” 'The Facts of Perception' (1878) in The Selected Writings of Hermann von Helmholtz, Ed. R. Karl, Middletown: Wesleyan University Press, 1971 p. 384

17. Thank you And thanks to collaborators: Rick Adams Andre Bastos Sven Bestmann Harriet Brown Jean Daunizeau Mark Edwards Xiaosi Gu Lee Harrison Stefan Kiebel James Kilner Jérémie Mattout Rosalyn Moran Will Penny Lisa Quattrocki Knight Klaas Stephan And colleagues: Andy Clark Peter Dayan Jörn Diedrichsen Paul Fletcher Pascal Fries Geoffrey Hinton James Hopkins Jakob Hohwy Henry Kennedy Paul Verschure Florentin Wörgötter And many others

18. Searching to test hypotheses – life as an efficient experiment Free energy principle minimise uncertainty

19. Time-scale Free-energy minimisation leading to… Perception and Action: The optimisation of neuronal and neuromuscular activity to suppress prediction errors (or free-energy) based on generative models of sensory data. Learning and attention: The optimisation of synaptic gain and efficacy over seconds to hours, to encode the precisions of prediction errors and causal structure in the sensorium. This entails suppression of free-energy over time. Neurodevelopment: Model optimisation through activity-dependent pruning and maintenance of neuronal connections that are specified epigenetically Evolution: Optimisation of the average free-energy (free-fitness) over time and individuals of a given class (e.g., conspecifics) by selective pressure on the epigenetic specification of their generative models.